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The paper presents an iterative algorithm for studying a nonlinear shallow-water wave equation. The equation is written as an evolution equation, involving only first-order spatial derivatives, coupled with the Helmholtz equation. We propose a two-step iterative method that first solves the evolution equation by the implicit midpoint rule and then solves… (More)

The OpenMP/OpenACC framework is proposed for solving the three-dimensional two-phase incompressible Navier-Stokes equations. The conservative phase-field method is employed for the interface transport equation. To reduce the calculation time, the Poisson equation solver for pressure correction term is applied to GPU computation by using the OpenACC… (More)

We investigate solution properties of a class of evolutionary partial differential equations (PDEs) with viscous and inviscid regularization. An equation in this class of PDEs can be written as an evolution equation, involving only first-order spatial derivatives, coupled with the Helmholtz equation. A recently developed two-step iterative method (Chiu et… (More)

The paper presents a sixth-order numerical algorithm for studying the completely integrable Camass-Holm (CH) equation. The proposed sixth-order accurate method preserves both the dispersion relation and the Hamiltonians of the CH equation. The CH equation in this study is written as an evolution equation, involving only the first-order spatial derivatives,… (More)

A two-step interface capturing scheme, implemented within the framework of conservative level set method, is developed in this study to simulate the gas/water two-phase fluid flow. In addition to solving the pure advection equation, which is used to advect the level set function for tracking interface, both nonlinear and stabilized features are taken into… (More)

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